rpubs_spatial
Bartlomiej Kowalczuk & Michal Thor
13 06 2020
Spatial analysis of Kensington and Chelsea district in London (on OA level) - including house prices.
Model part
Finding neighbours:
Global Spatial Autocorrelation
Moran I Test:
##
## Moran I test under randomisation
##
## data: OA.Census$employed
## weights: listw
##
## Moran I statistic standard deviate = 14.574, p-value < 2.2e-16
## alternative hypothesis: greater
## sample estimates:
## Moran I statistic Expectation Variance
## 0.3543126571 -0.0015873016 0.0005963801Employed has 0.34 moran statistic so it has a slight postitive autocorrelation - we may say that the data does spatially cluster.
Local Spatial Autocorrelation
LISA cluster map
GETIS-ORD
## Variable(s) "gstat" contains positive and negative values, so midpoint is set to 0. Set midpoint = NA to show the full spectrum of the color palette.
Linear model - employed
Using backward variables selection we eliminated most of the insignificant variables and came up with following model:
##
## Call:
## lm(formula = OA.Census$employed ~ . - 1, data = OA.Census[, sig_cols_2])
##
## Residuals:
## Min 1Q Median 3Q Max
## -28.3137 -3.2513 0.3911 3.7125 19.6324
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## white 0.31933 0.02140 14.923 < 2e-16 ***
## black_african 0.28316 0.05154 5.494 5.71e-08 ***
## single 0.12605 0.01913 6.588 9.44e-11 ***
## lowest_quali 0.58775 0.10107 5.815 9.65e-09 ***
## highest_quali 0.54895 0.02709 20.267 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 5.733 on 626 degrees of freedom
## Multiple R-squared: 0.992, Adjusted R-squared: 0.9919
## F-statistic: 1.548e+04 on 5 and 626 DF, p-value: < 2.2e-16
GWR - employed
## Adaptive q: 0.381966 CV score: 20668.69
## Adaptive q: 0.618034 CV score: 20832.37
## Adaptive q: 0.236068 CV score: 20444.63
## Adaptive q: 0.145898 CV score: 20428.7
## Adaptive q: 0.1756323 CV score: 20424.39
## Adaptive q: 0.1743792 CV score: 20424.91
## Adaptive q: 0.1987167 CV score: 20425.05
## Adaptive q: 0.1863925 CV score: 20421.06
## Adaptive q: 0.1910999 CV score: 20420.96
## Adaptive q: 0.1893096 CV score: 20419.23
## Adaptive q: 0.1887771 CV score: 20419.24
## Adaptive q: 0.1890814 CV score: 20419.23
## Adaptive q: 0.1899934 CV score: 20419.2
## Adaptive q: 0.1904161 CV score: 20419.66
## Adaptive q: 0.1897322 CV score: 20419.21
## Adaptive q: 0.1901549 CV score: 20419.2
## Adaptive q: 0.1902546 CV score: 20419.35
## Adaptive q: 0.1900932 CV score: 20419.2
## Adaptive q: 0.1901956 CV score: 20419.24
## Adaptive q: 0.1901549 CV score: 20419.2## Call:
## gwr(formula = OA.Census$employed ~ . - 1, data = OA.Census[,
## sig_cols_2], adapt = GWRbandwidth, hatmatrix = TRUE, se.fit = TRUE)
## Kernel function: gwr.Gauss
## Adaptive quantile: 0.1901549 (about 119 of 631 data points)
## Summary of GWR coefficient estimates at data points:
## Min. 1st Qu. Median 3rd Qu. Max. Global
## white 0.270580 0.288871 0.299836 0.313213 0.335517 0.3193
## black_african 0.023445 0.195534 0.242522 0.281999 0.351382 0.2832
## single 0.027817 0.052734 0.085185 0.213740 0.313398 0.1260
## lowest_quali 0.207876 0.276701 0.792704 0.904568 1.053125 0.5878
## highest_quali 0.462734 0.496910 0.596113 0.614051 0.651189 0.5490
## Number of data points: 631
## Effective number of parameters (residual: 2traceS - traceS'S): 22.44898
## Effective degrees of freedom (residual: 2traceS - traceS'S): 608.551
## Sigma (residual: 2traceS - traceS'S): 5.564811
## Effective number of parameters (model: traceS): 16.77853
## Effective degrees of freedom (model: traceS): 614.2215
## Sigma (model: traceS): 5.539064
## Sigma (ML): 5.464925
## AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21): 3970.666
## AIC (GWR p. 96, eq. 4.22): 3950.797
## Residual sum of squares: 18845.07
## Quasi-global R2: 0.6938792
LINEAR MODEL - PRICES
##
## Call:
## lm(formula = OA.Census.mp$mean_price ~ ., data = OA.Census.mp[sig_cols])
##
## Residuals:
## Min 1Q Median 3Q Max
## -2221130 -437500 -119641 227375 6426924
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6183339 735000 8.413 3.64e-16 ***
## single -12374 4913 -2.519 0.01207 *
## muslim -17097 7559 -2.262 0.02411 *
## highest_quali 12094 5790 2.089 0.03721 *
## jewish 70316 23129 3.040 0.00248 **
## asian -7480 9048 -0.827 0.40879
## one_car -38962 9201 -4.234 2.70e-05 ***
## no_cars -44399 7206 -6.161 1.42e-09 ***
## Age_30_44 -12502 9360 -1.336 0.18220
## employed -15271 7348 -2.078 0.03817 *
## private_rent 5909 3734 1.582 0.11415
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 860500 on 537 degrees of freedom
## Multiple R-squared: 0.3998, Adjusted R-squared: 0.3886
## F-statistic: 35.76 on 10 and 537 DF, p-value: < 2.2e-16
GWR - PRICES
## Adaptive q: 0.381966 CV score: 4.210973e+14
## Adaptive q: 0.618034 CV score: 4.182034e+14
## Adaptive q: 0.763932 CV score: 4.172618e+14
## Adaptive q: 0.9032981 CV score: 4.168388e+14
## Adaptive q: 0.9602445 CV score: 4.167327e+14
## Adaptive q: 0.9384929 CV score: 4.167674e+14
## Adaptive q: 0.9754298 CV score: 4.16696e+14
## Adaptive q: 0.9848148 CV score: 4.16671e+14
## Adaptive q: 0.990615 CV score: 4.166489e+14
## Adaptive q: 0.9941998 CV score: 4.166265e+14
## Adaptive q: 0.9964153 CV score: 4.166109e+14
## Adaptive q: 0.9977845 CV score: 4.165974e+14
## Adaptive q: 0.9986307 CV score: 4.165924e+14
## Adaptive q: 0.9991538 CV score: 4.16591e+14
## Adaptive q: 0.9995096 CV score: 4.1659e+14
## Adaptive q: 0.9996969 CV score: 4.165894e+14
## Adaptive q: 0.9998127 CV score: 4.165891e+14
## Adaptive q: 0.9998842 CV score: 4.165889e+14
## Adaptive q: 0.9999285 CV score: 4.165888e+14
## Adaptive q: 0.9999285 CV score: 4.165888e+14## Call:
## gwr(formula = OA.Census.mp$mean_price ~ ., data = OA.Census.mp[,
## sig_cols], adapt = GWRbandwidth, hatmatrix = TRUE, se.fit = TRUE)
## Kernel function: gwr.Gauss
## Adaptive quantile: 0.9999285 (about 547 of 548 data points)
## Summary of GWR coefficient estimates at data points:
## Min. 1st Qu. Median 3rd Qu. Max. Global
## X.Intercept. 6088655.0 6120270.2 6166817.8 6319731.2 6344257.2 6183339.3
## single -12875.8 -12827.6 -12476.1 -12242.1 -12106.5 -12373.7
## muslim -18901.7 -18208.7 -17912.6 -17555.4 -17225.3 -17096.8
## highest_quali 11117.2 11480.6 11588.8 11737.1 12170.0 12094.0
## jewish 65184.9 66420.8 67963.5 70085.6 71072.1 70316.2
## asian -7583.5 -7500.8 -7284.7 -7204.3 -7159.6 -7479.5
## one_car -40864.5 -40397.0 -38314.1 -37765.0 -37536.6 -38961.7
## no_cars -45261.9 -44957.5 -44167.7 -43936.7 -43719.8 -44399.1
## Age_30_44 -14652.5 -13714.0 -13312.8 -12977.9 -12410.5 -12501.7
## employed -15235.4 -14847.0 -14650.6 -14381.1 -13797.6 -15271.2
## private_rent 5505.2 5679.7 6169.0 6293.5 6343.6 5908.7
## Number of data points: 548
## Effective number of parameters (residual: 2traceS - traceS'S): 13.47969
## Effective degrees of freedom (residual: 2traceS - traceS'S): 534.5203
## Sigma (residual: 2traceS - traceS'S): 860638.4
## Effective number of parameters (model: traceS): 12.30621
## Effective degrees of freedom (model: traceS): 535.6938
## Sigma (model: traceS): 859695.2
## Sigma (ML): 849987.5
## AICc (GWR p. 61, eq 2.33; p. 96, eq. 4.21): 16546.15
## AIC (GWR p. 96, eq. 4.22): 16531.13
## Residual sum of squares: 3.959183e+14
## Quasi-global R2: 0.402407
Interpolation
##
## PLEASE NOTE: The components "delsgs" and "summary" of the
## object returned by deldir() are now DATA FRAMES rather than
## matrices (as they were prior to release 0.0-18).
## See help("deldir").
##
## PLEASE NOTE: The process that deldir() uses for determining
## duplicated points has changed from that used in version
## 0.0-9 of this package (and previously). See help("deldir").
Inverse distance weighting
## [inverse distance weighted interpolation]3D PLOTTING
Geostatistical interpolation
